A consumer products magazine indicated that the average life of a refrigerator before replacement is μ = 14 years with a (95% of data) range from 10 to 18 years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal. (a) The empirical rule indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ – 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ – 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviation For a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value – low value 4where it is estimated that about 95% of the commonly occurring data values fall into this range. Use this "rule of thumb" to approximate the standard deviation of x values. (Round your answer to one decimal place.) yr (b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? (Round your answer to four decimal places.) (c) What is the probability that someone will keep a refrigerator more than 18 years before replacement? (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A consumer products magazine indicated that the average life of a refrigerator before replacement is μ = 14 years with a (95% of data) range from 10 to 18 years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal.

(a) The empirical rule indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ – 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ – 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.

Estimating the standard deviation

For a symmetric, bell-shaped distribution,

standard deviation ≈

range

≈

high value – low value

where it is estimated that about 95% of the commonly occurring data values fall into this range.

Use this "rule of thumb" to approximate the standard deviation of x values. (Round your answer to one decimal place.)
yr

(b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? (Round your answer to four decimal places.)

(c) What is the probability that someone will keep a refrigerator more than 18 years before replacement? (Round your answer to four decimal places.)

(d) Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Suppose that a company guarantees refrigerators and will replace a refrigerator that breaks while under guarantee with a new one. However, the company does not want to replace more than 10% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?
yr

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